Active twist hollow beam system

ABSTRACT

A system for actively controlling the span-wise rotational twist of a hollow beam along its longitudinal axis, including a hollow beam structure having a leading edge and a trailing edge region, the beam being split along its length, an actuator arranged between split surfaces of the beam, the actuator adapted to move the split surfaces in a longitudinal direction relative to each other, inducing a twist in the beam. In one embodiment, the actuator is a plurality of thermal expansion material blocks alternating with mechanical compression blocks, the thermal expansion material blocks being heated to cause expansion in the spanwise longitudinal direction. Other alternative actuators include a rotary actuators such as a threaded screw, piezoelectric or magnetostrictive blocks, a hydraulic actuator, or a pneumatic actuator. In an embodiment, the beam is an airfoil shape.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a nonprovisional application under 35 U.S.C. §119(e)of provisional application No. 61/084,356, filed on Jul. 29, 2008, whichis incorporated herein by reference in its entirety.

BACKGROUND

1. Field of the Invention

This invention is related generally to a method for inducing span-wisetwist in hollow beams such as airfoils or rotor blades using a shearwarp actuator that is integrated into the beam along its span.

2. Related Technology

Most airfoil blades, once made, cannot change their twist (relativecross-section rotational) along the blade span. Many non-rotating bladesystems (e.g., airplane wings and control surfaces) have no built-intwist, whereas many of the rotating airfoil blade systems (e.g.,helicopter rotor blades) have some fixed amount of twist built intothem. Recent research and development has been focused on active twistcontrol of helicopter rotor blade systems primarily for mitigation ofaerodynamically-induced vibrations, as discussed in Chopra, I., “Statusof Application of Smart Structures Technology to Rotorcraft Systems”, J.Amer. Helicopter Soc., Vol. 45, No. 4, 2000, pp. 228-252, andGiurgiutiu, V. “Recent Advances in Smart-Material Rotor ControlActuation”, AIAA Paper #2000-1709, in Proc. 41st AIAA/ASME/ASCE.AHS/ASCStructures, Structural Dynamics, and Materials Conference, Atlanta, Ga.

Some developments in active control of rotor blade twist are describedin: Chen, P., and Chopra, I., “Hover Testing of Smart Rotor withInduced-Strain Actuation of Blade Twist”, AIAA Journal, Vol. 35, 1997;Wilbur, M. et al., “Hover Testing of the NASA/Army/MIT Active TwistRotor Prototype Blade”, AHS 56th Annual Forum, May 2000; Bothwell, C. etal., “Torsional Actuation with Extension-Torsion Composite Coupling anda Magnetostrictive Actuator”, AIAA Journal, Vol. 33, 1995; Derham, R. etal., “Design Evolution of an Active Materials Rotor”, in Proc. AHS 57thAnnual Forum, May 2001; and Jacot et al., U.S. Patent No. 6,065,934,entitled “Shape Memory Rotary Actuator”. U.S. Pat. No. 6,970,773 toPhillips discloses a system for inducing an optimized twist distributionfor a wing. U.S. Pat. No. 5,681,014 to Palmer discloses a torquetube-based system for twisting an airfoil. U.S. Pat. No. 5,505,589 toBergey discloses a controllable variable twist rotor blade assembly forrotary wing aircraft. U.S. Pat. No. 6,024,325 to Carter, Jr. discloses acoil-spring system for controlling pitch of a rotor for a rotary wingaircraft. U.S. Pat. No. 6,065,934 to Jacot et al. discloses a shapememory rotary actuator for a rotor blade. U.S. Pat. No. 6,497,385 toWachpress et al. discloses a rotor blade with optimized twistdistribution.

These active twist systems typically use piezoelectric ormagnetostrictive actuators embedded in the composite structure ofclosed-section rotor blades. The large torsional rigidity of the closedcross-section blades requires large actuation forces to achieve a givendegree of twist. Active-twist designs with structure-embedded actuationhave so-far been limited to a few degrees of twist or less over thelength of the blade. Deformation of closed-section beams by embedded orexternal actuators requires large amounts of actuation force and energybecause of the large elastic stiffness and strain energy associated withthe deforming member under twist.

SUMMARY

An embodiment of the invention is directed to an active twist hollowbeam system having a hollow beam that is split along the longitudinallength of the beam, and an actuator arranged to move split surfaces ofthe beam in a longitudinal direction relative to each other along thelength of the beam, inducing a twist in the beam. The actuator can bearranged between split surfaces of the beam. The beam can be an aircraftpropellor, wing, control surface, or rotor blade.

The beam can be a helicopter rotor blade, turbine blade, underwatervehicle control surface, or robotic appendage.

The system can include a plurality of shear-warp actuators, eachactuator arranged at a beam section at a different longitudinal positionalong the beam, each actuator independently controlled to inducedifferent twist amounts to the beam sections.

The actuator can include a number of thermal expansion material blocksarranged to expand in the longitudinal direction of the beam and movethe split surfaces relative to each other in the longitudinal direction.The actuator can also include an electrical resistance coil in contactwith the thermal expansion blocks. The actuator can also include aplurality of mechanical compression blocks, arranged in an alternatingpattern with the thermal expansion blocks.

The actuator can include thermal actuator blocks and an electricalresistance coil, piezoelectric or magnetostrictive material blocks, ahydraulic actuator, a pneumatic actuator, or a threaded screw extendingalong the longitudinal direction of the hollow beam.

An embodiment of the system is directed to an active twist hollow beamsystem including a hollow beam that is split along the longitudinallength of the beam, and a rotary actuator arranged in an interior of thebeam and extending along the longitudinal direction of the beam. Therotary actuator is axially fixed with respect to a first one of thesplit surfaces, the rotary actuator being matingly engaged with a secondone of the split surfaces, wherein turning the rotary actuator moves thesplit surfaces of the beam in a longitudinal direction relative to eachother along the length of the beam, inducing a twist in the beam.

The rotary actuator can include a threaded screw extending in thelongitudinal direction of the beam, the threaded screw axially fixedwith respect to a first one of the split surfaces, the threaded screwhaving a thread matched to an internal thread of a second one of thesplit surfaces, wherein turning the threaded screw moves the secondsplit surface in a longitudinal direction with respect to the firstsplit surface. The split surfaces of the beam can be restricted inmotion to the longitudinal direction.

Additional details will be apparent from the following Brief Descriptionof the Drawings and Detailed Description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrates an active twist hollow beam system inaccordance with an embodiment of the invention.

FIG. 2 illustrates warping behavior of an open-section beam under atorsional moment T.

FIG. 3 illustrates warping behavior of a closed-section beam under atorsional moment T.

FIGS. 4 and 5 illustrate material and geometric parameters of open andclosed section beams, respectively.

FIGS. 6A and 6B illustrate a thermally-based actuator for an activetwist system in accordance with an embodiment of the invention.

FIG. 7 is a graph illustrating thermal expansion coefficient, α, versuselastic modulus, E, for materials suitable for a thermal actuationelement in accordance with an embodiment of the invention.

FIG. 8 illustrates an exemplary active twist airfoil system with athermal expansion actuation system.

FIG. 9 illustrates a prototype open-beam split-trailing edge D-sparairfoil beam for demonstrating warp-twist behavior.

FIGS. 10A and 10B illustrate experimental results for the D-spar airfoilbeam of FIG. 9.

FIGS. 11A, 11B, and 11C illustrate an exemplary active twist hollow beamsystem with a thermal expansion actuation system.

FIG. 12 illustrates a hollow beam with three sections extending in thespanwise direction, each of which is independently controlled with aseparate shear-warp actuator.

FIGS. 13 and 14 illustrate some different embodiments of single anddouble-section active twist beam systems.

FIGS. 15A and 15B illustrate a screw-based shear-warp actuator forinducing warp displacement in hollow beam with a split along itslongitudinal extent.

FIGS. 16A and 16B show a NACA-0012 airfoil beam used for finite elementanalysis.

FIGS. 17A and 17B show the results of an applied warping displacementanalysis at the midspan and tip of the airfoil beam.

FIGS. 18A and 18B show the zero warping points on the airfoil beam.

FIGS. 19A and 19B show of the results from the applied torsion coupleanalysis at the midpoint and tip of the airfoil beam of FIG. 16A-16B.

FIG. 20 shows the axial stresses at the root of the airfoil beam for theapplied torsion couple analysis.

FIG. 21 shows how the twist angle θ is measured from the chord of theairfoil.

FIG. 22 plots the spanwise distribution of twist for case I, the appliedwarping analysis case, and case II, the applied torsion couple analysiscase.

FIG. 23A-23D show the warping displacements in the applied warping caseand the applied torsion case at midspan and tip of the blade.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention are directed to an active twist system thatpermits the use of low actuator loads/power to achieve a large degree ofspan-wise twist in a beam. The active twist system described hereinavoids storing significant amounts of elastic strain energy in the beamunder twisting, or “rotational” deformations.

The active twist system can be incorporated into any hollow beam. FIGS.1A and 1B illustrates an active twist system 10 in accordance with anembodiment of the invention in which the beam is a spar section for anairfoil. The hollow spar beam 11 has a leading edge 12 and a trailingedge 13 opposite the leading edge. The trailing edge 13 is splitlengthwise along the span of the spar beam, with two planar surfaces 14and 15 separated by a space. When the planar sections 14 and 15 aredisplaced in opposite directions along the lengthwise (span-wise) axisof the airfoil (x axis), the resulting out-of-plane warping deformationsinduce an angular twist of the spar beam.

As shown in FIG. 1B, a shear-warp actuator 16 is positioned between thebeam edges 17 and 18 along the span of the beam 11.

To form the hollow spar beam 11 of FIG. 1B, a lengthwise strip ofmaterial can be removed from a closed-section hollow airfoil beam andthe strip can be replaced by a shear-warp actuator that controls therelative lengthwise shear displacement (warp) between the edges 17 and18 of the cut along the span of the beam 11.

Alternatively, the airfoil beam 11 can initially be formed to have aseparation or split along the longitudinal length or span of the beam,so no material is required to be removed.

As shown in FIGS. 1A and 1B, the trailing edge 13 of the spar beam 11 issplit at a midpoint along the trailing edge. However, the location forthe split can be selected based on mechanical loading state of the beam,center-of-gravity position, centrifugal loading effects, and otherfactors. The split can be located anywhere on the cross section,including at other positionsin the trailing edge, on the leading edge,or in one of the planar surfaces 14 and 15. The torsional stiffness ofthe active twist beam system (spar beam plus integrated actuator) willdepend on the hollow beam's material properties and geometry and theactuator's geometry and material stiffness properties.

When energized, the shear-warp actuator 16 moves the beam sections 14and 15 in opposite directions along the span of the beam in the positiveand negative directions. This warp, or displacement, of the beamsections 14 and 15 in opposite directions, twists the hollow beam 11 asshown in FIG. 2. There is a discontinuous jump in the warp displacementon each side of the cut or split, and there are three points A, B, and Con the cross-section that experience no warping displacement.

In contrast, for a hollow closed-section beam 20 in FIG. 3, the warpingdisplacement under an applied torque, T, varies continuously, withoutany discontinuities or jumps, and there are four points E, F, G, and Hon the cross-section that experience no warping (zero-warp points). Themagnitude of the warping displacement for the hollow open-section beam11 of FIG. 2 is much larger than that experienced by hollowclosed-section beam of FIG. 3 for a given applied torque.

The active twist system 10 described herein exhibits characteristics ofboth open-section and closed-section beams. The requiredforce-displacement characteristics of the shear-warp actuator aregoverned by the open-section beam mechanics. The torsional stiffness ofthe combined open-section beam 11 plus shear-warp actuator 16 isgoverned by the beam materials and geometry and the actuator stiffness.The warping stiffness of the actuator 16 can be selected so that thetorsional stiffness of the combined open-section beam with integratedshear-warp actuator equals or exceeds the torsional stiffness of theequivalent closed-section beam.

The shear-warp actuator 16 is integrated with the beam 11 throughphysical connection at the cross-section cut edges 17 and 18. It issuitable to match the shear stiffness of the shear-warp actuator 16 (inthe activated and non-activated states) to that of the equivalentmaterial in a closed-section beam if the apparent torsional stiffness ofthe active twist airfoil system is to equal that of its closed-sectionequivalent. The elastic strain energy per unit length of a torsionalspring, k_(torsion)θ², is proportional to its elastic stiffness,k_(torsion), and the square of the twist per unit length, θ.

The active twist hollow beam system 10 uses small out-of-plane warpingdisplacements to achieve a given level of beam twist by taking advantageof the naturally low elastic torsional stiffness of an open beam (i.e.,one with a lengthwise cut) relative to that of an otherwise identicalclosed-section beam. The torsional stiffness of open-section beams canbe one-tenth or less that of closed-section beams with equivalentdimensions, and hence, the amount of elastic strain energy locked intothe beam structure during twist is one-tenth or less that of suchclosed-section equivalents. Actuator weight, size, and powerrequirements can be important factors governing the viability of anactive twist system.

The shear-warp actuator 16 for the active twist system can tailor thewarping force-displacement behavior and the apparent shear stiffness.The shear-warp actuator 16 can be a thermal actuator, a screw-basedactuator, a piezoelectric actuator, or another type of actuator that cangenerate shear displacement and has controllable shear stiffness.

The center of the beam 11 is preferably hollow, or partially hollow, soas to allow the airfoil to warp. Some interior structure can be present,depending on the warping force-displacement and shear stiffnessrequirements of a particular application. For example, rotor blades canhave a foam core or a honeycomb structure in their interior.

Approximate relationships between the relative warping displacement atthe longitudinal cut along the trailing edge of the beam 11, shear-flow,and beam twist of an open-section beam that is symmetric about thez-axis can be derived from mechanics by the following equation, in whichw is the warp displacement, A_(BAR) is the median enclosed area, θ isthe twist per unit length, T is the applied torque, G is the shearmodulus, L_(p) is the cross-section perimeter length, t is the materialthickness, and q is the shear flow acting along any lengthwise cut thatis equivalent to the applied torque T. These parameters are shown inFIGS. 4 and 5 for open-section beams and closed-section beams,respectively.

$\begin{matrix}{w = {{2\; A_{BAR}\theta} = {{6\; A_{BAR}\frac{T}{{GL}_{p}t^{3}}} = {\frac{12\; A_{BAR}^{2}}{{GL}_{p}t^{3}}q}}}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

Equation (1) defines the shear force-warping displacement (q-w)characteristics of the open-section beam that must be matched to theshear-warp actuator, and the design parameters shown in equations(5)-(7) can be used to design an actuator that meets the required q-wcharacteristics.

For the closed-section beam, relationships between the warpingdisplacement, shear-flow, and beam twist can also be derived. Thewarping displacement is w(s) at location s on the cross section, T isthe applied torque, A_(OS) is the area swept by a line connecting thecross-section's shear center to a point on the cross-section startingfrom the point on the cross-section where the z-axis intersects, A_(BAR)is the median enclosed area, q is the shear flow acting along anyimaginary lengthwise cut that is equivalent to the applied torque, and θis the twist per unit length. The relationships between the warpingdisplacement, shear-flow, and beam twist can be described by:

$\begin{matrix}{{{w(s)} = {{\frac{T\;\delta}{2\; A_{OS}}\left( {\frac{\delta_{OS}}{\delta} - \frac{A_{OS}}{A_{BAR}}} \right)} = {{\delta\left( {\frac{\delta_{OS}}{\delta} - \frac{A_{OS}}{A_{BAR}}} \right)}q}}}{and}} & {{Equation}\mspace{14mu}(2)} \\{\theta = {\frac{\delta}{2\; A_{OS}}q\mspace{14mu}{where}}} & {{Equation}\mspace{14mu}(3)} \\{\delta = {{\oint{\frac{\mathbb{d}s}{Gt}\mspace{14mu}{and}\mspace{14mu}\delta_{OS}}} = {\int_{0}^{s}{\frac{\mathbb{d}s}{Gt}.}}}} & {{Equation}\mspace{14mu}(4)}\end{matrix}$

For a open beam section, having a portion of the trailing edge replacedby a warp actuator, equations (2) and (4) determine the requiredactuator stiffness that would be equivalent to the beam materialreplaced by the warp actuator. These equations can be used to designactuators that meet the warping stiffness requirements for a particularapplication.

The material in the trailing edge of the closed section beam crosssection of FIG. 5, located between ±s, centered at the intersection ofthe Z axis with the trailing edge, has an apparent warping stiffness ofq/2w. The apparent warping stiffness can be matched by an actuatorintegrated with an open section beam. In performing the designcalculations, one can calculate 2 times w for the closed section beamwith a given applied torque, T, which is equivalent to a shear flow, q,at a distance s set equal to one-half of the actuator height.

Recall from FIGS. 2 and 3 that, for symmetric open-section beams, therewill be three points on the cross-section that experience no warping,and for symmetric closed-section beams, there will be four points on thecross-section that experience no warping. The exact locations of thezero-warping points on the cross section depends on the beam's materialand cross section geometry.

FIGS. 6A and 6B illustrates a section of an exemplary thermal actuator30 for inducing warp in a beam such as the FIG. 1 beam 11. An upperframe 31 has ribs (e.g., ridges or protrusions) 33, 34, and 35 extendingbetween alternating expansion elements and contraction elements, so eachrib has an expansion element on one side and contraction element on theopposite face of the rib. For example, rib 34 has a contraction element42 on one side and an expansion element 45 on the opposite side.Similarly, the lower frame 36 has ribs 37 and 38, with each rib arrangedwith an expansion element on one side and a contraction element on theother side. For example, rib 37 has a contraction element 41 on one sideand an expansion element 45 on the other side.

The thermal expansion elements 44, 45, and 46 can be heated withelectrical resistance coils or another suitable heating unit. When heatis removed from the expansion elements, they cool and return to theiroriginal dimensions, allowing the frames 31 and 36 to return to theirat-rest unactuated positions. The coils can be controlled by a singlecontroller, to apply uniform heat to each of the expansion elements.Alternatively, multiple actuators can independently control differentsections of the beam, as shown in FIG. 12.

The thermal expansion elements and mechanical contraction elements aremechanically opposed and alternate in their connection with the upperframe 31 and lower frame 36. Localized heating of the alternatingexpansion elements causes frame shear via thermal expansion of theexpansion elements and contraction of the mechanical contractionelements in a spanwise direction (along the longitudinal x axis). FIG.6B shows thermal expansion elements 44, 45, and 46 expanding in the xdirection when heated, pushing the lower frame 36 in one direction (−xdirection, to the left in FIG. 6A), and pushing the upper frame 31 inthe opposite direction (+x direction, to the right in FIG. 6A). As theupper and lower frames move in opposite x directions, the frame ribsmechanically compress the compression elements in the x direction.

In an exemplary embodiment, the thermal expansion elements andmechanical compression elements are affixed to the frame ribs withadhesive or mechanical fasteners, in order to prevent the frames fromshifting away from each other in the y or z directions. Alternatively,some or all of the expansion and contraction elements can remainunbonded to the frame. If the elements are not bonded to the frame, someother device for preventing the frames from moving in the y and zdirections, such as a linear bearing, can be included.

Note that FIGS. 6A and 6B show only the expansion elements as includingresistance heating coils. In other embodiments, all the elements includeresistance heating coils. When needed, only half of the elements areheated, and the other half of the elements are not heated, in analternating pattern, so the heated elements act as the expansionelements, and the unheated elements act as the compression elements. Thedirection of warp/twist can be selected by choosing which elements willexpand and which will contract.

The amount of warping displacement that results from a given change intemperature depends on the materials and geometry of the thermalactuation components. The actuator parameters can be selected to obtaina specific warping displacement for a given change in temperature andspecific (apparent) shear stiffness.

Assuming that the upper frame 31 and the lower frame 36 are rigid, thedisplacement or warping w can be predicted by equation (5). The warpingdisplacement is W, α₁ is the thermal expansion coefficient of theexpansion elements, E₁ is the elastic modulus of the expansion elements,L₁ is the length of the expansion element in the x direction, A₁ is thecross-sectional area of the expansion element, ΔT₁ is the change intemperature of the expansion element material. The term α₂ is thethermal expansion coefficient of the compression element, E₂ is theelastic modulus of the compression elements, L₂ is the length of thecompression element in the x direction, A₂ is the cross-sectional areaof the compression element, ΔT₁ is the change in temperature of theexpansion element, ΔT₂ is the change in temperature of the compressionelement material. The term q is the applied shear flow, which equals theapplied shear force, F, divided by the length, L₁+L₂. For the conditionin which the expansion element is heated (ΔT₁>0) and the compressionelement has no temperature change (ΔT₂=0),

$\begin{matrix}{w = {{\left\lbrack \frac{\alpha_{1}A_{1}{E_{1}\left( \frac{L_{1}L_{2}}{A_{2}E_{2}} \right)}}{L_{1} + {L_{2}\left( \frac{A_{1}E_{1}}{A_{2}E_{2}} \right)}} \right\rbrack \times \Delta\; T_{1}} + {\left\lbrack \frac{\left( {L_{1} + L_{2}} \right)\left( \frac{L_{1}L_{2}}{A_{2}E_{2}} \right)}{L_{1} + {L_{2}\left( \frac{A_{1}E_{1}}{A_{2}E_{2}} \right)}} \right\rbrack \times q}}} & {{Equation}\mspace{14mu}(5)}\end{matrix}$

It is preferable that the actuator have very small warping displacementwhen all parts of the actuator are subjected to the same temperaturechange (i.e., when ΔT₁=ΔT₂=ΔT≠0), to avoid twist in response to smallchanges in ambient temperature. Analysis of the warp-actuator underuniform temperature changes and zero external warping forces (i.e., q=0)leads to:

$\begin{matrix}{w = {\left\lbrack \frac{{\alpha_{1}A_{1}E_{1}} - {\alpha_{2}A_{2}E_{2}}}{\frac{A_{1}E_{1}}{L_{1}} + \frac{A_{2}E_{2}}{L_{2}}} \right\rbrack \times \Delta\; T}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

Note that if α₁A₁E₁−α₂A₂E₂=0, there will be zero warping under uniformtemperature changes. Therefore, one method of achieving zero warpingunder uniform temperature changes is to select identical materials andcross-sectional areas for the expansion material block and thecompression material block. In this example, α₁=α₂=α, A₁=A₂=A, andE₁=E₂=E. This leads to the following simplification for the warpingdisplacement, which can be used to design a shear actuator for an activetwist beam system:

$\begin{matrix}{w = {{\left\lbrack \frac{\alpha\; L_{1}L_{2}}{L_{1} + L_{2}} \right\rbrack \times \Delta\; T} + {\left\lbrack \frac{L_{1}L_{2}}{AE} \right\rbrack \times q}}} & {{Equation}\mspace{14mu}(7)}\end{matrix}$

Specific applications for the active twist system of FIG. 1 includecantilevered applications like aircraft wings, control surfaces,propellors, or helicopter rotor-blades having one end of the airfoilattached at the helicopter rotor hub. In cantilever applications, theactive-twist hollow beam system should be mechanically anchored at thezero warping points, to the maximum extent possible, in order tominimize any warping restraint that will alter the open-section beamwarping force-displacement characteristics. In an actual active twistsystem, there may be some degree of warping restraint imposed at theexternal connections due to the difficulty inherent in mechanicallyanchoring at exact point connections. The particular configuration ofthe connection can be an important aspect of the system design.Non-ideal connections (i.e., those that impose warping restraint) canrequire an actuator force above that predicted by Equation (5), tocompensate for the warping restraint and achieve the desired twist.

Selection of materials and dimensions for the thermal actuators thatprovide the desired twist and stiffness characteristics can be madebased on material properties such as thermal expansion coefficient, α,versus elastic modulus, E. Each material will have a restriction on themaximum temperature that can be used to affect thermal actuation. Theissues of how to best to heat the expanding elements to affect actuationand possible heat-transfer considerations (e.g., need for insulation) tominimize the required heating power and heat transfer to other parts ofthe system must also be addressed in the design of these types ofembodiments of the active-twist hollow beam airfoil system. Suitabletables or graphs of material properties can be used to select materialswith a high thermal expansion coefficient and sufficiently high elasticmodulus. FIG. 7 shows the Ashby “Materials Performance” plot of thermalexpansion coefficient, α, versus elastic modulus, E, suitable foridentifying materials for the thermal actuator system. The AshbyMaterials Performance plot information can be found in “Ashby, M. F.,Materials Selection in Mechanical Design, 2nd Ed. Butterworth-Heinemann,Oxford, 1999”.

In exemplary embodiments, the thermal expansion elements are engineeringelastomers and polymers such as neoprene, butyl, LDPE, HDPE, PP, PS, PC,PMMA, polyesters, epoxies, and MEL with a relatively high linearexpansion coefficient α.

FIG. 8 illustrates the thermal actuation system of FIGS. 6A and 6B in anactive twist beam system 60. A frame 65 is affixed to the trailing edgeplanar surface 62, and the opposite frame 66 is affixed to the trailingedge planar surface 63. Compression elements 68 and expansion elements67 are arranged alternatingly between the protrusions of the frames 65and 66, so that application of heat to the expansion elements causes theframe 65 and affixed airfoil trailing planar surface 62 to move in thepositive x direction and the frame 66 and affixed airfoil trailingplanar surface 63 to move in the negative x direction, causing a warpingdisplacement (twist) in the airfoil shape.

As shown herein, the frames 65 and 66 of the warp actuator are affixedto the trailing edge planar surfaces 62 and 63. In other embodiments, noframes are needed, and the airfoil trailing edge planar surfaces areshaped with ridges or protrusions, with the expansion and compressionelements being in direct contact with the airfoil structure.

FIG. 9 illustrates a prototype D-spar beam 170 with a split trailingedge surface. The term D-spar is used to describe the shape of the crosssection, although different cross section shapes are also suitable. TheD-spar is a spar-beam for an airfoil section, capable of supporting allloads (e.g., aerodynamic, centrifugal, etc.) on the airfoil.

The FIG. 9 prototype beam 170 can be used to estimate the amount of warpresulting from linear displacement of opposing portions of the trailingedge structure. The prototype D-Spar is made of aluminum and sized toachieve a torsional stiffness, GJ, approximately equal to 20,000N-m/(rad/m). Total length of the D-Spar beam is 34.5 inches. No warpactuator is installed for testing the D-spar, however, a linear bearing(not shown) is located in the vertical cut section between trailing edgesections 171 and 172 to restrict relative motion along the cut tospan-wise warping. The trailing edge sections 171 and 172 are verticalspar walls at the trailing edge of the D-spar beam. Material tabsattached to the inner and outer sides of the vertical spar walls of theD-Spar extend from each end of the D-spar.

For the FIG. 9 beam, the A_(BAR)≈0.5π(0.688)²+(1.435)(3.59)=5.895 in²=38cm², L_(P)≈1.348+3.695+π(0.688)+3.59+1.297=12.091 in=30.7 cm, and L=34.5in=87.6 cm, and t_(BAR)≈0.219(0.122)+0.603(0.089)+0.179(0.111)=0.1in=0.254 cm, where t_(BAR) is a weighted average thickness term thataccounts for the different thicknesses of the trailing edge sections andthe rest of the D-spar beam.

Warping loads are applied by pulling the material tabs in opposingdirections along the longitudinal axis of the D-spar. The D-Sparprototype is designed with a goal of an active twist capability of 0.032rad/m.

An Instron mechanical load-frame and accompanying instrumentation isused to measure the mechanical response of the prototype D-spar. Thewarping surfaces of the D-spar are attached to a load frame through theextended material tabs. A tensile load is applied, and the crossheaddisplacement and rotation of the top and bottom of the beam aremeasured. The Instron load frame has a 1000 lb load cell for measuringthe applied warping force. The top D-Spar warp-tab is pinned to theload-frame through a chain and clevis attachment to allow for rotation.The bottom warp-tab is pinned to the load-frame through a rigid clevisattachment. The test is conducted under crosshead displacement controlat an extension rate of 0.002 in/min. The test is interrupted every0.005 inch of extension for approximately 30 sec to allow for beamrotation measurements. A total of ten load-rotation measurements aretaken over a total warping displacement of 0.050 in.

Laser pointers are mounted on the top and bottom of the beam lying inthe cross-section plane. Each laser pointer is projected to ameasurement ruler (millimeter decrements) mounted approximately 7.5 ftaway, and relative displacement between the top and bottom is used tocalculate the beam twist, φ, where Δ is the distance (mm) between thecurrent and starting laser projection locations on the ruler, and d isthe distance from the center of rotation of the beam to the ruler. Inthis demonstration, d for the top part is 2413 mm and d for the bottompart is 2286 mm). The beam twist is φ=tan⁻¹(Δ/d). Total beam twist isthe sum of the top and bottom beam twists.

As seen in FIG. 10A and FIG. 10B, the prototype D-Spar exhibitsapproximately 0.05 in of warping displacement and 5.0 deg of beam twistwhen 150 lbs warping load is applied. These numbers result in a measuredwarping stiffness, k_(warp) of 3000 lbf/in (525 N/mm) and warp-rotationratio, k_(w-r) of 0.01 in/deg (14.6 mm/rad). These two stiffnessquantities are related to the beam geometry and materials throughequations (8) and (9), in which the warping force is q×L, and the beamtwist is θ×L , where L is the length of the beam.

$\begin{matrix}{k_{warp} = {\frac{q \times L}{w} = {\frac{{GL}_{p}t^{3}}{12\; A_{BAR}^{2}} \times L}}} & {{Equation}\mspace{14mu}(8)} \\{k_{w - r} = {\frac{w}{\theta \times L} = \frac{2\; A_{BAR}}{L}}} & {{Equation}\mspace{14mu}(9)}\end{matrix}$

Equations (8) and (9) produce a warping stiffness k_(warp) of 687 N/mmand a warp-rotation ratio k_(w-r) of 8.7 mm/rad, for the FIG. 9 D-sparformed from 7075-T6 aluminum. The calculated value of warping stiffnessk_(warp) is 31% higher and the calculated value of k_(w-r) is 41% lowerthan the experimentally determined values. Several factors maycontribute to the discrepancies between the measured stiffness and thepredicted stiffness. First, the application of warping loads through theexternal tabs at each end of the beam is non-ideal. The tabs are notcoaxial, which produces a bending moment that tends to separate the tabsin the chord direction. This tab separation motion will be added to thewarp displacement measured by the test machine creating an apparentincrease in the warp displacement per unit rotation, as observed (i.e.,14.6-vs-8.7 mm/rad). It also creates an apparent increase in the warpdisplacement per unit load, or an apparent decrease in the observedwarping stiffness (i.e., 525-vs-687 N/mm). Another possible factor isthe rotational constraint imposed by the mechanical connection betweenthe D-Spar loading tabs and the load frame. The presence of a resistingtorque will decrease the rotation for a given warp displacement orconversely, increase the warp displacement for a given rotation (i.e.,14.6 vs. 8.7 mm/rad). These factors are likely contributors to thedisagreement between calculations and experimental data.

FIGS. 11A, 11B, and 11C illustrate an active twist airfoil system 69with integrated shear actuator in accordance with an embodiment of theinvention. Two degrees of twist are achieved by an approximately 1 mlong prototype with the application of a warping load of 210 Ndistributed uniformly along the span.

FIG. 11A is a cross sectional view of the airfoil, with a fairingsection 71 positioned aft of the warp actuators 72 and 73 to minimizedrag. The hollow portion of the airfoil can be filled with foam 74 oranother lightweight material. A balance weight 75 can be located closeto the leading edge of the airfoil.

FIG. 11B is a cutaway view of the airfoil 69, showing the two warpactuators as including alternating thermal expansion elements andcompression elements arranged to push the central planar section 81 inthe positive x direction, and to push the two surrounding planarsections 82 and 83 in the negative x direction, warping the airfoil 69.

FIG. 11C is a cross sectional view of the airfoil with the warpactuators 72 and 73 in place.

The size of the thermal shear actuators in can be determined usingEquations (7) and (1) for warping. The beam provides an elastic warpingresistance q to the actuator according to the following Equation (10):

$\begin{matrix}{q = {{{- \frac{{GL}_{p}t^{3}}{12\; A_{BAR}^{2}}}w} = {- {kw}}}} & {{Equation}\mspace{14mu}(10)}\end{matrix}$

The following equation for the actuator warping displacement as afunction of temperature change for the thermal expansion material can beused to make design choices for the hollow beam D-spar system.

$\begin{matrix}{w = {\frac{\left\lbrack \frac{\alpha\; L_{1}L_{2}}{L_{1} + L_{2}} \right\rbrack}{1 + {\left\lbrack \frac{L_{1}L_{2}}{AE} \right\rbrack\left( \frac{{GL}_{p}t^{3}}{12\; A_{BAR}^{2}} \right)_{D - {Spar}}}} \times \Delta\; T_{1}}} & {{Equation}\mspace{14mu}(11)}\end{matrix}$

The following example illustrates how to size an actuator for a givenlength of a beam. A desired 1.8 degree/meter rotation θ in the beamcorresponds to a warping displacement w of 0.33 mm, according toEquation (1). Equation (11) leads to an expression involving theproperties α, E, L₁, L₂, A, ΔT₁ of the thermal actuator and the D-sparvariables.

The material to be used for the thermal expansion elements andcompression elements is selected from FIG. 7. The thermal expansioncoefficient and elastic modulus E for the selected material are foundfrom FIG. 7. As can be seen from FIG. 7, polyethylene has a high thermalexpansion coefficient compared to many other materials, and requiresreasonably small temperature differentials (ΔT) to achieve high warpingdisplacement.

Equation (11) predicts the temperature difference that would be requiredto achieve approximately 0.3 mm of warping displacement w correspondingto the 0.032 rad/m rotation θ desired for the system. For a low ormedium density polyethylene, the 0.3 mm of warping displacement can beachieved with a temperature differential that is well within thetemperature operating range for polyethylene (approximately 45 degreesC.).

The following example illustrates shows design calculations for athermally actuated D-spar, with representative results for a low/mediumdensity polyethylene (PE).

For this example, the following D-spar parameters are used: L_(P)=30.83cm; t=0.26 cm; A_(BAR)=47.29 cm²; G=2.7 GPa. The thermal actuatorgeometric parameters are: L₁=5 cm; D₁=2 cm; A₁=3.14 cm²; L₂=5 cm; D₂=2cm; A₂=3.14 cm². The thermal actuator material properties are:low/medium density polyethylene, linear copolymer; E₁=0.4 GPa; α₁=300μm/m/deg C.; E₂=0.4 GPa; Tmax=85 deg C.

Warping for different temperature differentials in the thermal expansionmaterial is calculated using the equation w=C₁(1+C₂k)⁻¹ΔT, whereC₁=α₁L₁L₂/(L₁+L₂) and k=GL_(P)t³/12A_(BAR) ².

C₁=7.5 μm/deg C.

C₂=1.989 μm/(N/m)

k=5.187×10⁵ m(N/m)

Actuator stiffness 1/C₂=50.27 MPa

Using these parameters, the warping displacement for different thermaldifferentials is calculated using the equation w=C₁(1+C₂k)⁻¹ΔT as:

ΔT (deg C.) w (mm) 100 0.7423 95 0.7052 90 0.6681 85 0.6310 80 0.5939 750.5568 70 0.5196 65 0.4825 60 0.4454 55 0.4083 50 0.3712 50 0.3712 450.3341 40 0.2969 35 0.2598 30 0.2227 25 0.1856 20 0.1485 15 0.1114 100.0742 5 0.0371 0 0.0000

Thus, a 0.3 mm warping displacement with an approximate 40 deg C.temperature differential can be achieved with polyethylene (PE) as thethermal actuator material for this particular actuator and D-Spar. Ascan be seen in FIG. 7, polyethylene has a very high coefficient ofthermal expansion relative to most other materials, although othermaterials with high coefficients of thermal expansion are also suitable.

The shear-warp actuators can be continuous along the beam span, with asingle controller, so the entire beam experiences the same amount oftwist per unit length.

Embodiments of the invention are also directed to hollow beams whichinclude several independently controlled shear-warp actuators. Theseseparate, independently controlled, shear-warp actuators can be arrangedat different locations along the longitudinal span of the beam, toachieve localized control of the beam twisting. For example, FIG. 12illustrates a beam with three segments 91, 92, and 93 extending in thelongitudinal or spanwise x direction, each of which can be separatelycontrolled with shear-warp actuators 94, 95, and 96. The shear-warpactuators can induce different warp displacements and different amountsof twist in the beam segments 91, 92, and 93 along the span.

FIGS. 13 and 14 show some different embodiments of active twist beamsystems. For example, FIG. 13 illustrates a single section beam 130 witha shear-warp actuator 131 arranged at the trailing edge of theairfoil-shaped beam. FIG. 14 illustrates an airfoil-shaped beam 132 witha shear-warp actuator 135 arranged at an intersection between a forwardsection 133 and an aft section 134 that induces warp in both the forwardsection and the aft section of the beam and a second shear-warp actuator36 arranged at the trailing edge. Note that only one actuator is needed(either 135 or 136) to affect twist in the two-section hollow beam. Thesame applies to hollow beams with more than two sections.

Other type of actuation elements can be used in-place of the thermalexpansion elements. Examples of suitable actuator types include but arenot limited to hydraulic, pneumatic, magnetostrictive, and piezoelectricactuators.

FIGS. 15A and 15B illustrate a screw-based shear-warp actuator forinducing warping displacement in hollow beam with a split along itslongitudinal extent. FIG. 15A is a cross sectional view, and FIG. 15B isan end view of the screw-driven active twist system. The system is apart of a larger rotor blade system, with a rotor shaft 115 supportingthe hub and attached rotor blade 100.

Rotation of the threaded screw 101 moves the upper beam section 111 in alongitudinal direction along the longitudinal length of the beam withrespect to the lower beam section 112, causing the beam to twist.

The threaded screw 101 is axially fixed to the lower beam planar surface112 with collars or pillow blocks 106 sandwiched between pairs of staysor lock collars 104 and 105. The threaded screw 101 also extends throughthe interior threads of the interior threaded nuts or collars 103, so asthe threaded screw 101 rotates, the interior threaded collars 103 arepushed in the positive or negative x direction. The interior threadedcollars 103 are fixed to the upper beam section 111, and thus, forcelinear translation of the upper beam section 111 in the positive ornegative x direction with respect to the lower beam section 112,inducing a warp and consequent twist in the beam 100.

The three points of zero warping are shown as points P, Q, and R. Thedimensional information and points-of-zero-warping correspond to thefabricated aluminum D-Spar prototype discussed above. The diameter ofthe threaded screw 101 can be sized to provide the necessary overalltorsional stiffness in the beam, for example, to recover the closedsection torsional stiffness of the beam.

It is not necessary that the threaded screw 101 be threaded for itsentire length. Exterior threads are necessary only where the screwsurface engages the threaded collars 103. The remaining portion of thescrew can be free of threads.

The threaded collars 103 are chemically or mechanically affixed to theupper beam surface 111, so spanwise motion of the collars warps upperbeam surface in a spanwise direction relative to the lower beam surface112. Alternatively, the threaded collars can be integrally formed withthe beam.

It is also envisioned that the system could use another rotary mechanisminstead of the threaded screw 101, as long as the rotary device extendedlongitudinally along the split portion of the beam and engaged matingsurfaces at several locations along the span of the beam.

As one example, helical cams with connecting rods arranged between thehelical cams can be used to induce twist in the beam. Rotating one endof a connecting rod turns the helical cams, inducing twist in the beam.As another example, moment arms with connecting rods arranged betweenthe moment arms can be used to induce twist in the beam. Rotating oneend of a connecting rod turns the moment arms, which are engaged with amechanism attached to one of the beam's planar surfaces, inducing thetwist in the beam.

The active twist beam system and methods described herein can be appliedto any hollow beam with a longitudinal split that allows relativelongitudinal motion between the split surfaces of the beam, and inparticular to hollow beams with a longitudinal section cut-out from thebeam with a shear actuator attached and acting between the two cutedges. The cross-sectional shape of the beam can be varied, and thelocation of the longitudinal cut or slit in the beam cross-section canbe varied.

The term hollow, as used herein, refers to beams with walls that arethin, where the wall thickness is less than the other beam dimensionssuch as height, width, and length. The hollow beam can have corematerials inside the hollow recesses, and can include thicker and/orstronger areas which may be desirable near the stress points of thebeam. The beam can be monocoque or semi-monocoque.

Finite element analysis of a cantilevered two-cell airfoil blade wasconducted on a NACA 0012 airfoil with an 8 inch (20.3 cm) chord and 8foot (2.44 m) span. The airfoil was made of 7075-T6 aluminum with thefairing skin thickness equal to 0.010 inch (0.25 mm) and the front sparwall thickness equal to 0.100 inch (2.5 mm). A horizontal cut 163 wasintroduced in the vertical spar section 161 and 162, as illustrated inFIG. 16A. FIG. 16B illustrates the “rib” stiffening applied at theairfoil tip using one row of rigid elements in the fairing section. Arow of rigid elements is employed at the outboard tip of the airfoil inthe fairing portion of the blade. The cut 163 forms sliding surfacesbetween the vertical spar sections 161 and 162, with the sections 161and 162 constrained to slide relative to each other only in the xdirection shown.

ABAQUS/Standard finite element code was used for the analysis. Anelastic, finite-strain formulation was used with 20-node hex (quadratic)elements. Joining the two sides of the spanwise cut in the spar areABAQUS slot-type connector elements (CONN3D2), which constrains relativemotion across the cut to warping displacements only (displacements alongdeformed x-axis, as illustrated in FIG. 16). The NACA 0012 geometry wasmeshed with Cubit, and there were approximately 1.7 million nodes and300,000 elements used in the analyses. The simulations were performed onan SGI Origin 3900 and SGI Altix 4700 with 4 active CPUs and 12 GBmemory. Runtime was approximately 4 hours/simulation.

Two cases were analyzed. In both cases, the airfoil was rigidly attached(cantilevered) at the root. In Case I, a linear increasing warpdisplacement was imposed, from zero to ±100 μm at the tip. In Case II, a50 N-m twisting couple was imposed at the tip through opposingtangential forces applied at the centerline of the vertical spar (2.25inches (5.7 cm) aft of the leading edge) on the outside surfaces of theairfoil. The results of the analysis are provided below.

FIGS. 17A and 17B and FIGS. 18A and 18B show of the results from theCase I (applied warping displacement) analysis. A warp of zero isapplied at the root and ±100 μm at the tip on the upper and lowersurfaces across the cut. FIG. 17A shows results for warping displacementversus twist at the 50% span positions (1.12 m from the root). FIG. 17Bshows results for warping displacement versus twist at the 100% spanposition (at tip, 2.299 m from root). As expected, the warping of thesliding surfaces is larger at the tip of the airfoil than at themidspan. As seen in FIG. 17A, some chordwise bending is observed at themidspan of the the airfoil section. This would be eliminated in anactual blade through the use of structural ribs in the airfoil section.Total blade twist at the tip for the imposed warping displacement was5.5 deg.

FIGS. 18A and 18B show the axial stresses at the root of the airfoil (ata point 0.003 meters, or about 0% along the airfoil span). The stressesindicated by the changes between dark and light shading representtransitions from positive to negative stress (passing through zero).Within the shaded transition areas, the stresses are within plus orminus 100 kPa. The results show that there are actually six locations onthe cross-section at the root that would experience zero warpingdeformation if the cross-section was not constrained at the root (oneeach at the leading edge and tail, and two each on the upper and lowersurfaces due to horizontal symmetry, indicated by letters I, J, K, L, M,and N.

FIGS. 19A and 19B show of the results from the Case II (50 N-m appliedtorsion couple) analysis, as warping displacement versus twist at the 50and 100% span positions, respectively. Little or no chordwise bendingwas observed this particular case. Total blade twist at the tip for theimposed twist couple of was 6 degrees, which is slightly more that thatexperienced in Case I.

FIG. 20 shows the axial stresses at the root for Case II, in which thestresses indicated by the changes between light and dark shadingrepresent transition from positive to negative stress (passing throughzero). The results are similar here, too, in that there are sixlocations on the cross-section at the root that experience zero warpingdeformations: one each at the leading edge and tail, and two each on theupper and lower surfaces symmetrically located (points S, T, U, V, W,and X).

FIG. 21-23 provide a comparison of blade twist between the two differentloading cases. FIG. 21 shows how the twist angle θ is measured from thechord. The twist is calculated using three points in the front sparsection. At the start, the twist angle is zero in every section, andthen varies along the span when the airfoil is deformed.

As seen in FIG. 22, the spanwise distribution of twist varies linearlyin Case II and non-linearly in Case I. Twist at the tip is nearlyidentical. Case I represents the concept of applying a warpingdeformation that increases linearly from root to tip to induce twist.

FIG. 23A-23D compare the warping displacements in the Case I and Case IIon the same scale, and illustrates that the warping displacement in CaseII at the tip is expected to be ˜50% of that in Case I for the sameapproximate degree of tip twist. FIG. 23A illustrates Case I (appliedlinear warp displacement) at midspan. FIG. 23B shows the Case I resultsat the tip of the blade. FIG. 23C illustrates Case II (applied endtorque) warping displacements at midspan. FIG. 23B shows the Case IIresults at the tip of the blade. The linear warping induces chordwisebending deformations of the airfoil. Case I has higher warpingdisplacements at the midspan and tip than Case II, with the highestwarping displacement at the Case I tip, as expected.

These finite element results provide additional confirmation thatspanwise warping displacement and blade twist are equivalent. Warpingdisplacements produce twist and twist produces warping displacements. Inthe current configuration, linear warping from zero to 0.2 mm at the tipproduced 5.5 deg of twist. For this two-section airfoil, there are sixlocations on the cross-section at the root that experience zero warping(FIGS. 18A, 18B, and 20). Structural connections at these points can beused to minimize warping constraint and the actuation force needed toaffect twist. The concept of using warping to induce twist has beenvalidated by this analysis, even with the blade fully anchored at theroot (Case I results). The unusual airfoil deformations observed can bemitigated using structural rib stiffeners as needed in the airfoilsection.

The following table lists some characteristics of some otheractive-twist system designs.

Maximum Blade Concept Team Twist Achieved Notes Embedded PZT wafersChopra et al. 0.4 deg @ 50 Hz Integral w/spar; in spar (UMD) 1.1 deg @90 Hz vibration control Active PZT fiber Wilbur et al. 2 deg @ 1 HzIntegral w/spar; composites (AFC) (NASA/Army/MIT) 1.5 deg @ 68 Hzvibration control Smart active blade tip Chopra et al. 2-2.5 deg @ 930RPM Flap at blade tip; (SABT) (UMD) vibration control Active materialsrotor; Derham et al. 0.6-1.4 deg @ hover Integral w/spar and integral &flap designs (Boeing/MIT) speed blade flap; vibration control ShapeMemory Jacot et al. 8 deg at Actuator, torque tube, Actuator Rotary(Boeing) <1 Hz lock; hover performance Actuator

Some previously developed methods for active twist control rely ontorsionally deforming closed-sections beam section through actuatorsembedded in the cross-section or by a coaxial torque actuator attachedbetween the outboard tip and beam root section. The large torsionalrigidity of these closed cross-sections requires large actuation forcesto achieve a given degree of twist. Some of the active-twist designswith structure-embedded actuation are limited to a few degrees of twistor less over the length of the blade. The twisting of closed-sectionbeams by embedded or other types of actuators requires large amounts ofactuation energy because of the large amount of elastic strain energyassociated with the twisting of a closed-section beam.

In contrast, the novel active twist system and method described hereintakes advantage of the significantly lower energy associated withelastic twist of open-section beams. This permits the use of loweractuator loads/power to achieve the same degree or greater twist withthe potential for actuator volume and weight savings and the potentialfor simple design and easier fabrication of the active twist airfoilsystems, including systems such as helicopter rotor blades and aircraftairfoils such as wings and control surfaces.

This system provides the ability to actively control the rotationaltwist of a hollow airfoil beam along its longitudinal axis, and requiressignificantly smaller forces to actuate the twist than other methods andcan be used to enhance the aerodynamic performance over variousoperational regimes. Active control of airfoil twist corresponds tolocalized changes in angle-of-attack, which can have a large influenceon the lift and drag forces. Applications include: improving helicopterrotor performance in hover and forward-flight, improving fixed-wingefficiency through reduced aerodynamic drag, improvements in air vehicleflight controls and water vehicle (surface and underwater) navigationcontrols through device design/construction simplification anddownsizing, turbine performance improvement through twist control of thefixed turbine stator blades, and new types of twisting robotic“appendages” that are simpler in design and construction and lighter inweight.

The invention has been described with reference to certain preferredembodiments. It will be understood, however, that the invention is notlimited to the preferred embodiments discussed above, and thatmodification and variations are possible within the scope of theappended claims.

1. An active twist hollow beam system comprising: a hollow beam, thebeam being split along a longitudinal length of the beam; and anactuator arranged to move a first split surface and a second splitsurface of the beam in a longitudinal direction relative to each otheralong the longitudinal length of the beam, inducing a twist in the beam,each of said split surfaces having a plurality of protrusions spacedapart along the longitudinal direction, the actuator comprising aplurality of solid thermal expansion blocks, each of the solid thermalexpansion blocks comprising elastomer or polymer, the actuator furtherincluding a plurality of mechanical compression blocks arranged in analternating pattern with the solid thermal expansion blocks, wherein, ofthe mechanical compression blocks and the solid thermal expansionblocks, only the solid thermal expansion blocks are in contact with anelectrical resistance heater, each of the solid thermal expansion blocksbeing located between and attached to at least one of the protrusions onthe first split surface and at least one of the protrusions on thesecond split surface, wherein in operation, for at least one of thesolid thermal expansion blocks, the electrical resistance heater heatsthe solid thermal expansion block, causing expansion of the solidthermal expansion block in the longitudinal direction, thereby movingthe split surfaces relative to each other in the longitudinal direction.2. The system of claim 1, wherein the actuator is arranged between thesplit surfaces of the beam.
 3. The system according to claim 1, whereinthe beam has an airfoil shape.
 4. The system according to claim 1,wherein the split along the longitudinal length of the beam is in atrailing edge of the beam.
 5. The system according to claim 1, whereinthe split along the longitudinal length of the beam is in a verticalspar of the beam.
 6. The system according to claim 1, wherein theactuator is a shear-warp actuator.
 7. The system according to claim 1,wherein the beam is an aircraft propeller, wing, control surface orrotor blade.
 8. The system according to claim 1, wherein the beam is ahelicopter rotor blade, turbine blade, underwater vehicle controlsurface, or robotic appendage.
 9. The active twist hollow beam systemaccording to claim 1, the system comprising a plurality of saidactuators, each actuator arranged at a beam section at a differentlongitudinal position along the beam, each actuator independentlycontrolled to induce different twist amounts to the beam sections. 10.The active twist hollow beam system of claim 1, the electricalresistance heater comprising an electrical resistance coil in contactwith the solid thermal expansion blocks.
 11. The active twist hollowbeam system of claim 1, wherein the thermal expansion blocks comprisepolyethylene.
 12. The active twist hollow beam system of claim 1,wherein the mechanical compression blocks and the thermal expansionblocks comprise polyethylene.
 13. The system according to claim 1, thebeam having a first longitudinal spit in a forward section of the beamand having a second longitudinal split in an after section of the beam,and the actuator arranged to move the split surfaces of the forward andafter sections of the beam in a longitudinal direction relative to eachother along the length of the beam, causing the forward and aftersections of the beam to warp.
 14. The active twist hollow beam system ofclaim 1, wherein said attachment of each of the thermal expansionelements to a protrusion on the first split surface and a protrusion ofa second split surface constrains the split surfaces from moving otherthan longitudinally with respect to each other.